OFFSET
1,2
COMMENTS
From Petros Hadjicostas, Aug 25 2019: (Start)
Both formulas below follow from the theory in the documentation of array A309951. We have Sum_{s = 0..A000041(3)} (-1)^s * A309951(3,s) * a(n-s) = 0, i.e., a(n) - 10*a(n-1) - 27*a(n-2) + 18*a(n-3) = 0 for n >= 4. This is a consequence of Eq. (6) on p. 248 of Abramson and Promislow (1978), where we let t=0 in the equation.
In the explicit formula by Vaclav Kotesovec below, a(n) = 6^n - 2*3^n + 1^n, the numbers 1, 3, 6 (that are raised to the n-th power) are the multinomial coefficients of the A000041(3) = 3 integer partitions of 3: 1 = 3!/3!, 3 = 3!/(1!2!), 6 = 3!/(1!1!1!).
(End)
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
Morton Abramson and David Promislow, Enumeration of arrays by column rises, J. Combinatorial Theory Ser. A 24(2) (1978), 247-250; see Eq. (6) on p. 248 (set t:=0).
FORMULA
Empirical: a(n) = 10*a(n-1) - 27*a(n-2) + 18*a(n-3).
Explicit formula: a(n) = 6^n - 2*3^n + 1. - Vaclav Kotesovec, May 31 2012
EXAMPLE
Some solutions for n=3:
1 2 0 2 1 0 0 2 1 1 2 0 1 2 0 2 1 0 1 2 0
2 0 1 2 0 1 2 0 1 2 0 1 0 2 1 2 0 1 1 0 2
0 2 1 0 1 2 2 1 0 2 1 0 2 0 1 0 2 1 0 2 1
CROSSREFS
KEYWORD
nonn
AUTHOR
R. H. Hardin, May 28 2012
STATUS
approved